(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     51268,       1536]
NotebookOptionsPosition[     48592,       1443]
NotebookOutlinePosition[     49369,       1473]
CellTagsIndexPosition[     49326,       1470]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 "Calculation of antenna pattern functions ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["F", "+"], TraditionalForm]], "None",
  FormatType->"TraditionalForm"],
 "and ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["F", "x"], TraditionalForm]], "None",
  FormatType->"TraditionalForm"],
 " \n"
}], "Title",
 CellFrame->{{0, 0}, {0.5, 0}},
 CellChangeTimes->{{3.458589289721652*^9, 3.458589361349268*^9}},
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Clear", "[", 
     RowBox[{
     "ThCap", ",", " ", "PhCap", ",", " ", "DetX", ",", " ", "DetY", ",", " ",
       "DetZ", ",", " ", "DetTensor", ",", " ", "m1", ",", " ", "m2", ",", 
      " ", "m3", ",", " ", "n1", ",", " ", "n2", ",", " ", "n3", ",", " ", 
      "mm", ",", " ", "mn", ",", " ", "nm", ",", " ", "nn"}], "]"}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Clear", "[", 
     RowBox[{
     "ePlus", ",", " ", "eCross", ",", " ", "DetTensorVec", ",", " ", "fPlus",
       ",", " ", "fCross"}], "]"}], ";"}], "\n", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"ThCap", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         RowBox[{"Cos", "[", "thD", "]"}]}], "*", 
        RowBox[{"Cos", "[", "phD", "]"}]}], ",", " ", 
       RowBox[{
        RowBox[{"-", 
         RowBox[{"Cos", "[", "thD", "]"}]}], "*", 
        RowBox[{"Sin", "[", "phD", "]"}]}], ",", " ", 
       RowBox[{"Sin", "[", "thD", "]"}]}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"PhCap", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Sin", "[", "phD", "]"}]}], ",", " ", 
       RowBox[{"Cos", "[", "phD", "]"}], ",", " ", "0"}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"DetX", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cos", "[", "psiD", "]"}], "*", "ThCap"}], " ", "+", " ", 
      RowBox[{
       RowBox[{"Sin", "[", "psiD", "]"}], "*", "PhCap"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"DetY", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Sin", "[", "psiD", "]"}]}], "*", "ThCap"}], " ", "+", " ", 
      RowBox[{
       RowBox[{"Cos", "[", "psiD", "]"}], "*", "PhCap"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"DetZ", " ", "=", " ", 
     RowBox[{"Simplify", "[", 
      RowBox[{"Cross", "[", 
       RowBox[{"DetX", ",", " ", "DetY"}], "]"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", "\n", 
   RowBox[{
    RowBox[{"DetTensor", " ", "=", " ", 
     RowBox[{"Simplify", "[", " ", 
      RowBox[{
       FractionBox["1", "2"], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"Transpose", "[", 
           RowBox[{"{", "DetX", "}"}], "]"}], ".", 
          RowBox[{"{", "DetX", "}"}]}], " ", "-", " ", 
         RowBox[{
          RowBox[{"Transpose", "[", 
           RowBox[{"{", "DetY", "}"}], "]"}], ".", 
          RowBox[{"{", "DetY", "}"}]}]}], ")"}]}], "]"}]}], ";"}], "\n", 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"m1", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Sin", "[", "phi", "]"}], "*", 
       RowBox[{"Cos", "[", "psi", "]"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"Cos", "[", "phi", "]"}], "*", 
       RowBox[{"Cos", "[", "theta", "]"}], "*", 
       RowBox[{"Sin", "[", "psi", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"m2", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Cos", "[", "phi", "]"}]}], "*", 
       RowBox[{"Cos", "[", "psi", "]"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"Sin", "[", "phi", "]"}], "*", 
       RowBox[{"Cos", "[", "theta", "]"}], "*", 
       RowBox[{"Sin", "[", "psi", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"m3", " ", "=", " ", 
     RowBox[{
      RowBox[{"Sin", "[", "theta", "]"}], "*", 
      RowBox[{"Sin", "[", "psi", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n1", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Sin", "[", "phi", "]"}]}], "*", 
       RowBox[{"Sin", "[", "psi", "]"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"Cos", "[", "phi", "]"}], "*", 
       RowBox[{"Cos", "[", "theta", "]"}], "*", 
       RowBox[{"Cos", "[", "psi", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n2", " ", "=", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cos", "[", "phi", "]"}], "*", 
       RowBox[{"Sin", "[", "psi", "]"}]}], " ", "-", " ", 
      RowBox[{
       RowBox[{"Sin", "[", "phi", "]"}], "*", 
       RowBox[{"Cos", "[", "theta", "]"}], "*", 
       RowBox[{"Cos", "[", "psi", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n3", " ", "=", " ", 
     RowBox[{
      RowBox[{"Sin", "[", "theta", "]"}], "*", 
      RowBox[{"Cos", "[", "psi", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"mm", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"m1", "*", "m1"}], ",", " ", 
       RowBox[{"m1", "*", "m2"}], ",", " ", 
       RowBox[{"m1", "*", "m3"}], ",", " ", 
       RowBox[{"m2", "*", "m1"}], ",", " ", 
       RowBox[{"m2", "*", "m2"}], ",", " ", 
       RowBox[{"m2", "*", "m3"}], ",", " ", 
       RowBox[{"m3", "*", "m1"}], ",", " ", 
       RowBox[{"m3", "*", "m2"}], ",", " ", 
       RowBox[{"m3", "*", "m3"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"mn", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"m1", "*", "n1"}], ",", " ", 
       RowBox[{"m1", "*", "n2"}], ",", " ", 
       RowBox[{"m1", "*", "n3"}], ",", " ", 
       RowBox[{"m2", "*", "n1"}], ",", " ", 
       RowBox[{"m2", "*", "n2"}], ",", " ", 
       RowBox[{"m2", "*", "n3"}], ",", " ", 
       RowBox[{"m3", "*", "n1"}], ",", " ", 
       RowBox[{"m3", "*", "n2"}], ",", " ", 
       RowBox[{"m3", "*", "n3"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"nm", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"n1", "*", "m1"}], ",", " ", 
       RowBox[{"n1", "*", "m2"}], ",", " ", 
       RowBox[{"n1", "*", "m3"}], ",", " ", 
       RowBox[{"n2", "*", "m1"}], ",", " ", 
       RowBox[{"n2", "*", "m2"}], ",", " ", 
       RowBox[{"n2", "*", "m3"}], ",", " ", 
       RowBox[{"n3", "*", "m1"}], ",", " ", 
       RowBox[{"n3", "*", "m2"}], ",", " ", 
       RowBox[{"n3", "*", "m3"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"nn", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"n1", "*", "n1"}], ",", " ", 
       RowBox[{"n1", "*", "n2"}], ",", " ", 
       RowBox[{"n1", "*", "n3"}], ",", " ", 
       RowBox[{"n2", "*", "n1"}], ",", " ", 
       RowBox[{"n2", "*", "n2"}], ",", " ", 
       RowBox[{"n2", "*", "n3"}], ",", " ", 
       RowBox[{"n3", "*", "n1"}], ",", " ", 
       RowBox[{"n3", "*", "n2"}], ",", " ", 
       RowBox[{"n3", "*", "n3"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"ePlus", " ", "=", " ", 
    RowBox[{"FullSimplify", "[", 
     RowBox[{"mm", " ", "-", " ", "nn"}], "]"}]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"eCross", " ", "=", " ", 
     RowBox[{"Simplify", "[", 
      RowBox[{"mn", " ", "+", " ", "nm"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", "\n", 
   RowBox[{
    RowBox[{"d11", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "1", "]"}], "]"}], "[", 
      RowBox[{"[", "1", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d21", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "[", 
      RowBox[{"[", "1", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d31", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "[", 
      RowBox[{"[", "1", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d12", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "1", "]"}], "]"}], "[", 
      RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d22", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "[", 
      RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d32", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "[", 
      RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d13", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "1", "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d23", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"d33", " ", "=", " ", 
     RowBox[{
      RowBox[{"DetTensor", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], ";"}], "\n", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"DetTensorVec", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
      "d11", ",", " ", "d21", ",", " ", "d31", ",", " ", "d12", ",", " ", 
       "d22", ",", " ", "d32", ",", "d13", ",", " ", "d23", ",", " ", "d33"}],
       "}"}]}], ";"}], "\[IndentingNewLine]", "\n", 
   RowBox[{
    RowBox[{"fPlus", "   ", "=", " ", 
     RowBox[{"Simplify", "[", 
      RowBox[{
       RowBox[{"{", "ePlus", "}"}], " ", ".", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", "DetTensorVec", "}"}], "]"}]}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"fCross", " ", "=", " ", 
     RowBox[{"Simplify", "[", 
      RowBox[{
       RowBox[{"{", "eCross", "}"}], " ", ".", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", "DetTensorVec", "}"}], "]"}]}], "]"}]}], 
    ";"}]}]}]], "Input",
 CellChangeTimes->{{3.458654674469944*^9, 3.45865473823225*^9}, {
  3.458654774771151*^9, 3.4586548227523003`*^9}, {3.45865864684053*^9, 
  3.4586586654594316`*^9}, {3.458658771954732*^9, 3.4586588068764544`*^9}, {
  3.4590263455769863`*^9, 3.459026375985651*^9}, {3.459090141001659*^9, 
  3.4590901809117727`*^9}, {3.45909022315874*^9, 3.459090223935792*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{"Cos", "[", "psi", "]"}], " ", 
        RowBox[{"Sin", "[", "phi", "]"}]}], "-", 
       RowBox[{
        RowBox[{"Cos", "[", "phi", "]"}], " ", 
        RowBox[{"Cos", "[", "theta", "]"}], " ", 
        RowBox[{"Sin", "[", "psi", "]"}]}]}], ")"}], "2"], "-", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{"Cos", "[", "phi", "]"}], " ", 
        RowBox[{"Cos", "[", "psi", "]"}], " ", 
        RowBox[{"Cos", "[", "theta", "]"}]}], "+", 
       RowBox[{
        RowBox[{"Sin", "[", "phi", "]"}], " ", 
        RowBox[{"Sin", "[", "psi", "]"}]}]}], ")"}], "2"]}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "4"]}], " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"(", 
      RowBox[{"3", "+", 
       RowBox[{"Cos", "[", 
        RowBox[{"2", " ", "theta"}], "]"}]}], ")"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "phi"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "phi"}], "]"}], " ", 
     RowBox[{"Cos", "[", "theta", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "psi"}], "]"}]}]}], ",", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Cos", "[", "phi", "]"}], " ", 
       RowBox[{"Cos", "[", 
        RowBox[{"2", " ", "psi"}], "]"}], " ", 
       RowBox[{"Cos", "[", "theta", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Sin", "[", "phi", "]"}], " ", 
       RowBox[{"Sin", "[", 
        RowBox[{"2", " ", "psi"}], "]"}]}]}], ")"}], " ", 
    RowBox[{"Sin", "[", "theta", "]"}]}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "4"]}], " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"(", 
      RowBox[{"3", "+", 
       RowBox[{"Cos", "[", 
        RowBox[{"2", " ", "theta"}], "]"}]}], ")"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "phi"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "phi"}], "]"}], " ", 
     RowBox[{"Cos", "[", "theta", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "psi"}], "]"}]}]}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"Cos", "[", "phi", "]"}], "2"], "-", 
       RowBox[{
        SuperscriptBox[
         RowBox[{"Cos", "[", "theta", "]"}], "2"], " ", 
        SuperscriptBox[
         RowBox[{"Sin", "[", "phi", "]"}], "2"]}]}], ")"}]}], "+", 
    RowBox[{
     RowBox[{"Cos", "[", "theta", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "phi"}], "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "psi"}], "]"}]}]}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      RowBox[{"Cos", "[", "phi", "]"}]}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"Sin", "[", "theta", "]"}]}], "+", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"Sin", "[", "phi", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "theta"}], "]"}]}]}], ",", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Cos", "[", "phi", "]"}], " ", 
       RowBox[{"Cos", "[", 
        RowBox[{"2", " ", "psi"}], "]"}], " ", 
       RowBox[{"Cos", "[", "theta", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Sin", "[", "phi", "]"}], " ", 
       RowBox[{"Sin", "[", 
        RowBox[{"2", " ", "psi"}], "]"}]}]}], ")"}], " ", 
    RowBox[{"Sin", "[", "theta", "]"}]}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      RowBox[{"Cos", "[", "phi", "]"}]}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"Sin", "[", "theta", "]"}]}], "+", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}], " ", 
     RowBox[{"Sin", "[", "phi", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "theta"}], "]"}]}]}], ",", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "psi"}], "]"}]}], " ", 
    SuperscriptBox[
     RowBox[{"Sin", "[", "theta", "]"}], "2"]}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.459026376541872*^9, {3.45909014517811*^9, 3.459090181401939*^9}, 
   3.4590902279880466`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "\nWe can always get the detector tensor by calling 'LoadDetectorData'. In \
this case we don't need explicit form of the DetTensor in terms of ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["\[Theta]", "D"], TraditionalForm]], "None",
  FormatType->"TraditionalForm"],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["\[Phi]", "D"], TraditionalForm]], "None",
  FormatType->"TraditionalForm"],
 " and ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["\[Psi]", "D"], TraditionalForm]], "None",
  FormatType->"TraditionalForm"],
 "."
}], "Section",
 CellChangeTimes->{{3.45865187269058*^9, 3.458651997728703*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Clear", "[", 
     RowBox[{
     "d11", ",", " ", "d21", ",", " ", "d31", ",", " ", "d21", ",", " ", 
      "d22", ",", " ", "d32", ",", " ", "d31", ",", " ", "d32", ",", " ", 
      "d33", ",", " ", "fPlus", ",", " ", "fCross"}], "]"}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"DetTensorVec", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
      "d11", ",", " ", "d21", ",", " ", "d31", ",", " ", "d12", ",", " ", 
       "d22", ",", " ", "d32", ",", "d13", ",", " ", "d23", ",", " ", "d33"}],
       "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"fPlus", " ", "=", " ", 
    RowBox[{"FullSimplify", "[", 
     RowBox[{
      RowBox[{"{", "ePlus", "}"}], " ", ".", 
      RowBox[{"Transpose", "[", 
       RowBox[{"{", "DetTensorVec", "}"}], "]"}]}], "]"}]}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"fCross", " ", "=", " ", 
     RowBox[{"Simplify", "[", 
      RowBox[{
       RowBox[{"{", "eCross", "}"}], " ", ".", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", "DetTensorVec", "}"}], "]"}]}], "]"}]}], 
    ";"}]}]}]], "Input",
 CellChangeTimes->{{3.458652001458503*^9, 3.4586520779849367`*^9}, 
   3.458652161210478*^9, {3.458654759260687*^9, 3.4586547625804157`*^9}, {
   3.458654878684813*^9, 3.4586548833681173`*^9}, {3.458670216456956*^9, 
   3.45867022536543*^9}, 3.4590242837205877`*^9, 3.459024343956956*^9, {
   3.459024801855369*^9, 3.459024802060655*^9}, {3.459024836406888*^9, 
   3.45902485076724*^9}, {3.459024881571621*^9, 3.459024944684658*^9}, {
   3.4590249776224537`*^9, 3.45902497876624*^9}, {3.459029521641108*^9, 
   3.459029522293709*^9}, 3.45902971509621*^9, {3.459029856393415*^9, 
   3.459029895347125*^9}}],

Cell[BoxData["$Aborted"], "Output",
 CellChangeTimes->{3.4590297155902233`*^9, 3.459030295520537*^9}],

Cell[BoxData["$Aborted"], "Output",
 CellChangeTimes->{3.4590297155902233`*^9, 3.4590303059517307`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"ab", " ", "=", " ", 
    RowBox[{"LinearSolve", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Cos", "[", 
           RowBox[{"2", " ", "psi"}], "]"}], ",", " ", 
          RowBox[{"Sin", "[", 
           RowBox[{"2", " ", "psi"}], "]"}]}], "}"}], ",", " ", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"-", 
           RowBox[{"Sin", "[", 
            RowBox[{"2", " ", "psi"}], "]"}]}], ",", " ", 
          RowBox[{"Cos", "[", 
           RowBox[{"2", " ", "psi"}], "]"}]}], "}"}]}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{"fPlus", "[", 
          RowBox[{"[", "1", "]"}], "]"}], "[", 
         RowBox[{"[", "1", "]"}], "]"}], ",", " ", 
        RowBox[{
         RowBox[{"fCross", "[", 
          RowBox[{"[", "1", "]"}], "]"}], "[", 
         RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], ";"}]}]], "Input",\

 CellChangeTimes->{{3.459024346251816*^9, 3.459024481770208*^9}, {
  3.459024666215417*^9, 3.459024674902947*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"FullSimplify", "[", 
   RowBox[{
    RowBox[{"ab", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "[", 
    RowBox[{"[", "2", "]"}], "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.459024676088375*^9, 3.459024695966922*^9}, {
  3.459025185242579*^9, 3.459025200679626*^9}, {3.45902526852671*^9, 
  3.459025268651479*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "2"}], " ", "d21", " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"2", " ", "phi"}], "]"}], " ", 
     RowBox[{"Cos", "[", "theta", "]"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"d11", "-", "d22"}], ")"}], " ", 
     RowBox[{"Cos", "[", "theta", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"2", " ", "phi"}], "]"}]}], "+", 
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"d32", " ", 
        RowBox[{"Cos", "[", "phi", "]"}]}], "-", 
       RowBox[{"d31", " ", 
        RowBox[{"Sin", "[", "phi", "]"}]}]}], ")"}], " ", 
     RowBox[{"Sin", "[", "theta", "]"}]}]}], ")"}], " ", 
  RowBox[{"Tan", "[", 
   RowBox[{"2", " ", "psi"}], "]"}]}]], "Output",
 CellChangeTimes->{3.459024702794132*^9, 3.4590248684634323`*^9, 
  3.459024990281892*^9, 3.459025189407229*^9, 3.459025221278206*^9, 
  3.459025271049823*^9, 3.4590297350817327`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"CForm", "[", 
   RowBox[{
    RowBox[{"fPlus", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.4586521861514177`*^9, 3.458652229303523*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"CForm", "[", 
   RowBox[{
    RowBox[{"fCross", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], "]"}], "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.458652518416657*^9, 3.4586525306817904`*^9}}],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"dFplusOverdTheta", " ", "=", " ", 
     RowBox[{"D", "[", 
      RowBox[{"fPlus", ",", " ", "theta"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"dFplusOverdPhi", " ", "=", " ", 
     RowBox[{"D", "[", 
      RowBox[{"fPlus", ",", " ", "phi"}], "]"}]}], ";"}]}]}]], "Input",
 CellChangeTimes->{{3.45865376581988*^9, 3.458653989114212*^9}}],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"dFCrossOverdTheta", " ", "=", " ", 
     RowBox[{"D", "[", 
      RowBox[{"fCross", ",", " ", "theta"}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"dFCrossOverdPhi", " ", "=", " ", 
     RowBox[{"D", "[", 
      RowBox[{"fCross", ",", " ", "phi"}], "]"}]}], ";"}]}]}]], "Input",
 CellChangeTimes->{{3.458654611704174*^9, 3.45865462854809*^9}}],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"AmpC", " ", "=", " ", 
     RowBox[{
      FractionBox["1", "2"], 
      SqrtBox[
       RowBox[{
        RowBox[{"4", " ", 
         SuperscriptBox[
          RowBox[{"Cos", "[", "iota", "]"}], "2"], " ", 
         SuperscriptBox["fCross", "2"]}], "+", 
        RowBox[{
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"1", " ", "+", " ", 
            SuperscriptBox[
             RowBox[{"Cos", "[", "iota", "]"}], "2"]}], ")"}], "2"], " ", 
         SuperscriptBox["fPlus", "2"], " "}]}]]}]}], ";"}], 
   "\[IndentingNewLine]", "\[IndentingNewLine]", "\n", 
   RowBox[{
    RowBox[{"Phi0", " ", "=", " ", 
     RowBox[{"ArcTan", "[", 
      FractionBox[
       RowBox[{"2", " ", "fCross", " ", 
        RowBox[{"Cos", "[", "iota", "]"}]}], 
       RowBox[{"fPlus", " ", 
        RowBox[{"(", 
         RowBox[{"1", " ", "+", " ", 
          SuperscriptBox[
           RowBox[{"Cos", "[", "iota", "]"}], "2"]}], ")"}]}]], "]"}]}], 
    ";"}]}]}]], "Input",
 CellChangeTimes->{{3.458670716127993*^9, 3.458670718718995*^9}, 
   3.45867165440121*^9, {3.458678230803237*^9, 3.458678247719338*^9}, {
   3.45867834627234*^9, 3.458678349810047*^9}, {3.4586785754489202`*^9, 
   3.4586785856625633`*^9}, {3.458678851526803*^9, 3.4586788533189917`*^9}, {
   3.458679040112953*^9, 3.458679044560994*^9}, {3.458679235589664*^9, 
   3.458679237602297*^9}, {3.459022516286221*^9, 3.459022523795083*^9}, 
   3.459022715338826*^9, 3.459022804368167*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"A", " ", "=", " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"a", ",", " ", "b"}], "}"}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"c", ",", " ", "d"}], "}"}]}], "}"}]}]}]], "Input",
 CellChangeTimes->{{3.4590239386276817`*^9, 3.459024016146319*^9}, {
  3.459024063090547*^9, 3.459024075866478*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"a", ",", "b"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"c", ",", "d"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.4590239926510277`*^9, 3.4590240166110497`*^9}, {
  3.459024064179348*^9, 3.45902407631656*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Inverse", "[", "A", "]"}]}]], "Input",
 CellChangeTimes->{{3.459024004926421*^9, 3.4590240083139277`*^9}, {
  3.459024054756177*^9, 3.4590240580716953`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     FractionBox["d", 
      RowBox[{
       RowBox[{
        RowBox[{"-", "b"}], " ", "c"}], "+", 
       RowBox[{"a", " ", "d"}]}]], ",", 
     RowBox[{"-", 
      FractionBox["b", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "b"}], " ", "c"}], "+", 
        RowBox[{"a", " ", "d"}]}]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["c", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "b"}], " ", "c"}], "+", 
        RowBox[{"a", " ", "d"}]}]]}], ",", 
     FractionBox["a", 
      RowBox[{
       RowBox[{
        RowBox[{"-", "b"}], " ", "c"}], "+", 
       RowBox[{"a", " ", "d"}]}]]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.459024008751656*^9, 3.459024018507654*^9}, {
  3.459024058469474*^9, 3.459024078313879*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Inverse", "[", 
   RowBox[{"{", 
    RowBox[{"a", ",", "b"}], "}"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.459024084630075*^9, 3.459024096010556*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Inverse", "::", "\<\"matsq\"\>"}], 
  RowBox[{
  ":", " "}], "\<\"Argument \\!\\({a, b}\\) at position \\!\\(1\\) is not a \
nonempty square matrix. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/message/General/matsq\\\", ButtonNote -> \
\\\"Inverse::matsq\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.459024097064093*^9}],

Cell[BoxData[
 RowBox[{"Inverse", "[", 
  RowBox[{"{", 
   RowBox[{"a", ",", "b"}], "}"}], "]"}]], "Output",
 CellChangeTimes->{3.459024097065588*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", 
  
  RowBox[{
   RowBox[{
    RowBox[{"P", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"p1", ",", " ", "q1", ",", " ", "r1"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"p2", ",", " ", "q2", ",", " ", "r2"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"p3", ",", " ", "q3", ",", " ", "r3"}], "}"}]}], "}"}]}], 
    ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"B", " ", "=", " ", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"Cos", "[", "\[Psi]", "]"}], 
           RowBox[{"Cos", "[", "\[Phi]", "]"}]}], " ", "-", " ", 
          RowBox[{
           RowBox[{"Cos", "[", "\[Theta]", "]"}], 
           RowBox[{"Sin", "[", "\[Phi]", "]"}], 
           RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ",", " ", 
         RowBox[{"-", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{
             RowBox[{"Sin", "[", "\[Psi]", "]"}], 
             RowBox[{"Cos", "[", "\[Phi]", "]"}]}], " ", "+", " ", 
            RowBox[{
             RowBox[{"Cos", "[", "\[Theta]", "]"}], 
             RowBox[{"Sin", "[", "\[Phi]", "]"}], 
             RowBox[{"Cos", "[", "\[Psi]", "]"}]}]}], ")"}]}], ",", " ", 
         RowBox[{
          RowBox[{"Sin", "[", "\[Theta]", "]"}], 
          RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"Cos", "[", "\[Psi]", "]"}], 
           RowBox[{"Sin", "[", "\[Phi]", "]"}]}], " ", "+", " ", 
          RowBox[{
           RowBox[{"Cos", "[", "\[Theta]", "]"}], 
           RowBox[{"Cos", "[", "\[Phi]", "]"}], 
           RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ",", " ", 
         RowBox[{
          RowBox[{
           RowBox[{"-", 
            RowBox[{"Sin", "[", "\[Psi]", "]"}]}], " ", 
           RowBox[{"Sin", "[", "\[Phi]", "]"}]}], " ", "+", " ", 
          RowBox[{
           RowBox[{"Cos", "[", "\[Theta]", "]"}], 
           RowBox[{"Cos", "[", "\[Phi]", "]"}], 
           RowBox[{"Cos", "[", "\[Psi]", "]"}]}]}], ",", " ", 
         RowBox[{
          RowBox[{"-", 
           RowBox[{"Sin", "[", "\[Theta]", "]"}]}], " ", 
          RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{
          RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
          RowBox[{"Sin", "[", "\[Psi]", "]"}]}], ",", " ", 
         RowBox[{
          RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
          RowBox[{"Cos", "[", "\[Psi]", "]"}]}], ",", " ", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}]}], 
    ";"}]}]}]], "Input",
 CellChangeTimes->{{3.4590881015438957`*^9, 3.459088295294159*^9}, {
   3.4590883256197567`*^9, 3.459088666377825*^9}, 3.459088701673316*^9, {
   3.459088733427362*^9, 3.45908883561522*^9}, {3.459088926831958*^9, 
   3.459088944738468*^9}, 3.459088990064834*^9}],

Cell[BoxData[
 TagBox[
  RowBox[{
   RowBox[{"A", " ", "=", " ", "B"}], "\[NoBreak]", ";"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Input",
 CellChangeTimes->{{3.459088906973363*^9, 3.4590889094966307`*^9}, {
  3.459088993788521*^9, 3.4590890073525143`*^9}, {3.459089539200761*^9, 
  3.459089539445302*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Fp", " ", "=", " ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}]}], " ", "-", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}]}]}]}], " ", "\[IndentingNewLine]", 
   RowBox[{"Fc", " ", "=", " ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}]}], " ", "-", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"A", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}]}]}]}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"ab", " ", "=", " ", 
     RowBox[{"LinearSolve", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"Cos", "[", "\[Psi]", "]"}], ",", " ", 
           RowBox[{"-", 
            RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], "}"}], ",", " ", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"Sin", "[", "\[Psi]", "]"}], ",", " ", 
           RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "}"}]}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"Fp", ",", " ", "Fc"}], "}"}]}], "]"}]}], ";"}]}]}]], "Input",\

 CellChangeTimes->{{3.45908900880752*^9, 3.459089032227055*^9}, {
  3.459089080864572*^9, 3.4590892413934517`*^9}, {3.4590893158578672`*^9, 
  3.4590893376883593`*^9}, {3.459090420484851*^9, 3.459090490416161*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Cos", "[", "\[Theta]", "]"}]}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "-", 
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "-", 
     RowBox[{
      RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}], "+", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "-", 
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.459090461231184*^9, 3.4590904917015657`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Cos", "[", "\[Theta]", "]"}]}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "-", 
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}], "+", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "-", 
     RowBox[{
      RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "-", 
     RowBox[{
      RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
      RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.459090461231184*^9, 3.4590904917099743`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"ab", "[", 
    RowBox[{"[", "1", "]"}], "]"}], "[", 
   RowBox[{"[", "2", "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.459089242707769*^9, 3.45908924773557*^9}, {
  3.459089289292205*^9, 3.459089295048541*^9}, {3.459089343094819*^9, 
  3.459089363141964*^9}, {3.459090495588135*^9, 3.459090506696807*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Psi]", "]"}], "3"], " ", 
   RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"], " ", 
   RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Psi]", "]"}], "3"], " ", 
   RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
  RowBox[{"3", " ", 
   RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Phi]", "]"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Psi]", "]"}], "2"], " ", 
   RowBox[{"Sin", "[", "\[Psi]", "]"}]}], "-", 
  RowBox[{
   RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Psi]", "]"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Phi]", "]"}], "2"], " ", 
   RowBox[{"Sin", "[", "\[Psi]", "]"}]}], "-", 
  RowBox[{
   RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
   RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
   RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Psi]", "]"}], "2"]}], "-", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"], " ", 
   RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
   RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
   RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Psi]", "]"}], "2"]}], "+", 
  RowBox[{
   RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Cos", "[", "\[Phi]", "]"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Psi]", "]"}], "3"]}], "+", 
  RowBox[{
   RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Phi]", "]"}], "2"], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", "\[Psi]", "]"}], "3"]}]}]], "Output",
 CellChangeTimes->{
  3.459089248167017*^9, 3.459089312771298*^9, 3.459089347648864*^9, 
   3.45908938381092*^9, 3.459089547342111*^9, {3.459090430668844*^9, 
   3.459090449860059*^9}, {3.459090500491892*^9, 3.459090507205349*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Simplify", "[", 
   RowBox[{"P", ".", "B"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.459088675442068*^9, 3.45908869425674*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"a", " ", "q1"}], "+", 
      RowBox[{"p1", " ", 
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "+", 
      RowBox[{"r1", " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}], "-", 
      RowBox[{"p1", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ",", 
     RowBox[{
      RowBox[{"b", " ", "q1"}], "-", 
      RowBox[{"p1", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"r1", " ", 
          RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "-", 
         RowBox[{"p1", " ", 
          RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"r1", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "q1"}], " ", 
          RowBox[{"Cos", "[", "\[Phi]", "]"}]}], "+", 
         RowBox[{"p1", " ", 
          RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}], ")"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"a", " ", "q2"}], "+", 
      RowBox[{"p2", " ", 
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "+", 
      RowBox[{"r2", " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}], "-", 
      RowBox[{"p2", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ",", 
     RowBox[{
      RowBox[{"b", " ", "q2"}], "-", 
      RowBox[{"p2", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"r2", " ", 
          RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "-", 
         RowBox[{"p2", " ", 
          RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"r2", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "q2"}], " ", 
          RowBox[{"Cos", "[", "\[Phi]", "]"}]}], "+", 
         RowBox[{"p2", " ", 
          RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}], ")"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"a", " ", "q3"}], "+", 
      RowBox[{"p3", " ", 
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}]}], "+", 
      RowBox[{"r3", " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}], "-", 
      RowBox[{"p3", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ",", 
     RowBox[{
      RowBox[{"b", " ", "q3"}], "-", 
      RowBox[{"p3", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Psi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"r3", " ", 
          RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "-", 
         RowBox[{"p3", " ", 
          RowBox[{"Sin", "[", "\[Psi]", "]"}]}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"r3", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "+", 
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"-", "q3"}], " ", 
          RowBox[{"Cos", "[", "\[Phi]", "]"}]}], "+", 
         RowBox[{"p3", " ", 
          RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}], ")"}]}]}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.459088677869225*^9, 3.4590887046039667`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"X", " ", "=", " ", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Cos", "[", "a", "]"}], ",", " ", 
        RowBox[{"-", 
         RowBox[{"Sin", "[", "a", "]"}]}], ",", " ", "0"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Sin", "[", "a", "]"}], ",", " ", 
        RowBox[{"Cos", "[", "a", "]"}], ",", " ", "0"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"0", ",", " ", "0", ",", " ", "1"}], "}"}]}], "}"}]}], 
   "\[IndentingNewLine]", 
   RowBox[{"Y", " ", "=", " ", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"1", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"0", ",", " ", 
        RowBox[{"Cos", "[", "b", "]"}], ",", " ", 
        RowBox[{"-", 
         RowBox[{"Sin", "[", "b", "]"}]}]}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"0", ",", " ", 
        RowBox[{"Sin", "[", "b", "]"}], ",", " ", 
        RowBox[{"Cos", "[", "b", "]"}]}], "}"}]}], "}"}]}]}]}]], "Input",
 CellChangeTimes->{
  3.459090083840314*^9, {3.4590905383649673`*^9, 3.459090647704418*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Cos", "[", "a", "]"}], ",", 
     RowBox[{"-", 
      RowBox[{"Sin", "[", "a", "]"}]}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Sin", "[", "a", "]"}], ",", 
     RowBox[{"Cos", "[", "a", "]"}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.459090631462174*^9, 3.459090649408019*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"Cos", "[", "b", "]"}], ",", 
     RowBox[{"-", 
      RowBox[{"Sin", "[", "b", "]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"Sin", "[", "b", "]"}], ",", 
     RowBox[{"Cos", "[", "b", "]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.459090631462174*^9, 3.459090649410043*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"X", ".", "Y"}], " ", "//", "MatrixForm"}]}]], "Input",
 CellChangeTimes->{{3.459090657306514*^9, 3.459090665442215*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"Cos", "[", "a", "]"}], 
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Cos", "[", "b", "]"}]}], " ", 
       RowBox[{"Sin", "[", "a", "]"}]}], 
      RowBox[{
       RowBox[{"Sin", "[", "a", "]"}], " ", 
       RowBox[{"Sin", "[", "b", "]"}]}]},
     {
      RowBox[{"Sin", "[", "a", "]"}], 
      RowBox[{
       RowBox[{"Cos", "[", "a", "]"}], " ", 
       RowBox[{"Cos", "[", "b", "]"}]}], 
      RowBox[{
       RowBox[{"-", 
        RowBox[{"Cos", "[", "a", "]"}]}], " ", 
       RowBox[{"Sin", "[", "b", "]"}]}]},
     {"0", 
      RowBox[{"Sin", "[", "b", "]"}], 
      RowBox[{"Cos", "[", "b", "]"}]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.459090658948924*^9, 3.4590906659092407`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"R", " ", "=", " ", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"a", ",", "b", ",", "c"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"p", ",", " ", "q", ",", " ", "r"}], "}"}], ",", " ", 
        RowBox[{"{", 
         RowBox[{"0", ",", " ", "m", ",", " ", "n"}], "}"}]}], "}"}], ".", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Cos", "[", "g", "]"}], ",", " ", 
          RowBox[{"-", 
           RowBox[{"Sin", "[", "g", "]"}]}], ",", " ", "0"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Sin", "[", "g", "]"}], ",", " ", 
          RowBox[{"Cos", "[", "g", "]"}], ",", " ", "0"}], "}"}], ",", " ", 
        RowBox[{"{", 
         RowBox[{"0", ",", " ", "0", ",", " ", "1"}], "}"}]}], "}"}]}]}], 
    ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"R", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"R", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}]}], " ", "-", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"R", "[", 
        RowBox[{"[", "1", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}], " ", 
      RowBox[{
       RowBox[{"R", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "[", 
       RowBox[{"[", "2", "]"}], "]"}]}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.459091349929592*^9, 3.459091468191201*^9}, {
  3.459091510060678*^9, 3.459091571964692*^9}, {3.459091749324555*^9, 
  3.459091765081192*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"a", " ", "p"}], "-", 
     RowBox[{"b", " ", "q"}]}], ")"}], " ", 
   RowBox[{"Cos", "[", 
    RowBox[{"2", " ", "g"}], "]"}]}], "+", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"b", " ", "p"}], "+", 
     RowBox[{"a", " ", "q"}]}], ")"}], " ", 
   RowBox[{"Sin", "[", 
    RowBox[{"2", " ", "g"}], "]"}]}]}]], "Output",
 CellChangeTimes->{
  3.459091426530699*^9, {3.459091456758224*^9, 3.459091468688715*^9}, {
   3.4590915163089447`*^9, 3.459091572607736*^9}, {3.459091751709097*^9, 
   3.459091766656332*^9}}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1157, 965},
WindowMargins->{{Automatic, 82}, {48, Automatic}},
FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (May 21, 2008)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> 
     FrontEnd`FileName[{"Creative"}, "PastelColor.nb", CharacterEncoding -> 
       "UTF-8"]], FontSize -> 18], 
   Cell[
    StyleData["Input"]], 
   Cell[
    StyleData["Input"]], 
   Cell[
    StyleData["Input"]], 
   Cell[
    StyleData[All]]}, Visible -> False, FrontEndVersion -> 
  "6.0 for Mac OS X x86 (32-bit) (May 21, 2008)", StyleDefinitions -> 
  "PrivateStylesheetFormatting.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 431, 15, 81, "Title"],
Cell[CellGroupData[{
Cell[1046, 42, 10147, 273, 687, "Input"],
Cell[11196, 317, 4565, 141, 204, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15798, 463, 624, 19, 112, "Section"],
Cell[CellGroupData[{
Cell[16447, 486, 1793, 40, 113, "Input"],
Cell[18243, 528, 101, 1, 37, "Output"],
Cell[18347, 531, 103, 1, 37, "Output"]
}, Open  ]],
Cell[18465, 535, 1136, 33, 53, "Input"],
Cell[CellGroupData[{
Cell[19626, 572, 375, 9, 53, "Input"],
Cell[20004, 583, 966, 27, 37, "Output"]
}, Open  ]],
Cell[20985, 613, 276, 7, 53, "Input"],
Cell[21264, 622, 277, 7, 53, "Input"],
Cell[21544, 631, 448, 12, 68, "Input"],
Cell[21995, 645, 452, 12, 68, "Input"],
Cell[22450, 659, 1566, 39, 169, "Input"],
Cell[CellGroupData[{
Cell[24041, 702, 382, 10, 53, "Input"],
Cell[24426, 714, 289, 8, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24752, 727, 215, 4, 53, "Input"],
Cell[24970, 733, 862, 30, 55, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25869, 768, 211, 5, 53, "Input"],
Cell[26083, 775, 444, 9, 23, "Message"],
Cell[26530, 786, 150, 4, 37, "Output"]
}, Open  ]],
Cell[26695, 793, 3049, 78, 113, "Input"],
Cell[29747, 873, 323, 8, 37, InheritFromParent],
Cell[CellGroupData[{
Cell[30095, 885, 2190, 64, 98, "Input"],
Cell[32288, 951, 1448, 42, 53, "Output"],
Cell[33739, 995, 1448, 42, 53, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[35224, 1042, 378, 8, 53, "Input"],
Cell[35605, 1052, 2132, 57, 59, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[37774, 1114, 186, 4, 53, "Input"],
Cell[37963, 1120, 4489, 124, 98, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[42489, 1249, 1198, 33, 68, "Input"],
Cell[43690, 1284, 480, 14, 37, "Output"],
Cell[44173, 1300, 480, 14, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[44690, 1319, 190, 4, 53, "Input"],
Cell[44883, 1325, 1257, 37, 86, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[46177, 1367, 1769, 50, 83, "Input"],
Cell[47949, 1419, 603, 19, 37, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
